Popularity trends of the NFL and NBA are fun and interesting for casual fans while also of critical importance for advertisers and businesses with an interest in the sports leagues. Sports leagues have clear and distinct seasons and these have a major impact on when each league is most popular. To measure the popularity of each league, we used search data from Google Trends that gives real-time and historical data on the relative popularity of search words. By using search volume to measure popularity, the times of year, a sport is popular relative to its season can be explained. It is also possible to forecast how sport leagues are trending relative to each other. We compared and discussed three different univariate models both theoretically and empirically: the trend plus seasonality regression, Holt- Winters Multiplicative (HWMM), and Seasonal Autoregressive Integrated Moving Average (SARIMA) models to determine the popularity trends. For each league, the six forecasting performance measures used in this study indicated HWMM gave the most accurate predictions.
For an integer k ≥ 1, we say that a (finite simple undirected) graph G is k-distance-locally disconnected, or simply k-locally disconnected if, for any x ∈ V (G), the set of vertices at distance at least 1 and at most k from x induces in G a disconnected graph. In this paper we study the asymptotic behavior of the number of edges of a k-locally disconnected graph on n vertices. For general graphs, we show that this number is Θ(n2) for any fixed value of k and, in the special case of regular graphs, we show that this asymptotic rate of growth cannot be achieved. For regular graphs, we give a general upper bound and we show its asymptotic sharpness for some values of k. We also discuss some connections with cages.